Breakdown of the Bardeen–Cooper–Schrieffer ground state at a quantum phase transition


Advances in solid-state and atomic physics are exposing the hidden relationships between conventional and exotic states of quantum matter. Prominent examples include the discovery of exotic superconductivity proximate to conventional spin and charge order1,2, and the crossover from long-range phase order to preformed pairs achieved in gases of cold fermions3,4,5 and inferred for copper oxide superconductors5. The unifying theme is that incompatible ground states can be connected by quantum phase transitions. Quantum fluctuations about the transition are manifestations of the competition between qualitatively distinct organizing principles6,7, such as a long-wavelength density wave and a short-coherence-length condensate. They may even give rise to ‘protected’ phases, like fluctuation-mediated superconductivity that survives only in the vicinity of an antiferromagnetic quantum critical point8,9. However, few model systems that demonstrate continuous quantum phase transitions have been identified, and the complex nature of many systems of interest hinders efforts to more fully understand correlations and fluctuations near a zero-temperature instability. Here we report the suppression of magnetism by hydrostatic pressure in elemental chromium, a simple cubic metal that demonstrates a subtle form of itinerant antiferromagnetism10,11,12,13,14,15,16 formally equivalent to the Bardeen–Cooper–Schrieffer (BCS) state in conventional superconductors. By directly measuring the associated charge order in a diamond anvil cell at low temperatures, we find a phase transition at pressures of 10 GPa driven by fluctuations that destroy the BCS-like state but preserve the strong magnetic interaction between itinerant electrons and holes. Chromium is unique among stoichiometric magnetic metals studied so far in that the quantum phase transition is continuous, allowing experimental access to the quantum singularity and a direct probe of the competition between conventional and exotic order in a theoretically tractable material.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Phase diagram and Brillouin zone schematic for magnetism in chromium.
Figure 2: Structure, CDW intensity and wavevector Q for T  < 8 K.
Figure 3: Dependence of Q on order parameter and band structure in the classical and quantum regimes.
Figure 4: Disparate routes to quantum criticality.


  1. 1

    de la Cruz, C. et al. Magnetic order close to superconductivity in the iron-based layered LaO1-x F x FeAs systems. Nature 453, 899–902 (2008)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Morosan, E. et al. Superconductivity in Cu x TiSe2 . Nature Phys. 2, 544–550 (2006)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Regal, C. A., Greiner, M. & Jin, D. S. Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett. 92, 040403 (2004)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Chin, C. et al. Observation of the pairing gap in a strongly interacting Fermi gas. Science 305, 1128–1130 (2004)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS-BEC crossover: from high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Sachdev, S. Quantum criticality: competing ground states in low dimensions. Science 288, 475–480 (2000)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Coleman, P. & Schofield, A. J. Quantum criticality. Nature 433, 226–229 (2005)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Nagaosa, N. Superconductivity and antiferromagnetism in high-TC cuprates. Science 275, 1078–1079 (1997)

    CAS  Article  Google Scholar 

  9. 9

    Broun, D. M. What lies beneath the dome? Nature Phys. 4, 170–172 (2008)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Fawcett, E. Spin-density-wave antiferromagnetism in chromium. Rev. Mod. Phys. 60, 209–283 (1988)

    ADS  CAS  Article  Google Scholar 

  11. 11

    McWhan, D. B. & Rice, T. M. Pressure dependence of itinerant antiferromagnetism in chromium. Phys. Rev. Lett. 19, 846–849 (1967)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Yeh, A. et al. Quantum phase transition in a common metal. Nature 419, 459–462 (2002)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Lee, M., Husmann, A., Rosenbaum, T. F. & Aeppli, G. High resolution study of magnetic ordering at absolute zero. Phys. Rev. Lett. 92, 187201 (2004)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Feng, Y. et al. Pressure-tuned spin and charge ordering in an itinerant antiferromagnet. Phys. Rev. Lett. 99, 137201 (2007)

    ADS  Article  Google Scholar 

  15. 15

    Jaramillo, R. et al. Chromium at high pressures: weak coupling and strong fluctuations in an itinerant antiferromagnet. Phys. Rev. B 77, 184418 (2008)

    ADS  Article  Google Scholar 

  16. 16

    Overhauser, A. W. Spin density waves in an electron gas. Phys. Rev. 128, 1437–1452 (1962)

    ADS  Article  Google Scholar 

  17. 17

    Young, C. Y. & Sokoloff, J. B. The role of harmonics in the first order antiferromagnetic to paramagnetic transition in chromium. J. Phys. F 4, 1304–1319 (1974)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Hill, J. P., Helgesen, G. & Gibbs, D. X-ray-scattering study of charge- and spin-density waves in chromium. Phys. Rev. B 51, 10336–10344 (1995)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Pfleiderer, C. Why first order quantum phase transitions are interesting. J. Phys. Condens. Matter 17, S987–S997 (2005)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Werner, S. A., Arrott, A. & Kendrick, H. Temperature and magnetic-field dependence of the antiferromagnetism in pure chromium. Phys. Rev. 155, 528–539 (1967)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Rice, T. M. Band-structure effects in itinerant antiferromagnetism. Phys. Rev. B 2, 3619–3630 (1970)

    ADS  Article  Google Scholar 

  22. 22

    Sokolov, D. A. et al. Elastic neutron scattering in quantum critical antiferromagnet Cr0. 963V0. 037 . Physica B (Amsterdam) 403, 1276–1278 (2008)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Schroder, A., Aeppli, G., Bucher, E., Ramazashvili, R. & Coleman, P. Scaling of magnetic fluctuations near a quantum phase transition. Phys. Rev. Lett. 80, 5623–5626 (1998)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Sweetland, E., Tsai, C.-Y., Wintner, B. A., Brock, J. D. & Thorne, R. E. Measurement of the charge-density-wave correlation length in NbSe3 by high-resolution X-ray scattering. Phys. Rev. Lett. 65, 3165–3168 (1990)

    ADS  CAS  Article  Google Scholar 

  25. 25

    DeLand, S. M., Mozurkewich, G. & Chapman, L. D. X-ray investigation of charge-density-wave pinning in blue bronze. Phys. Rev. Lett. 66, 2026–2029 (1991)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Gegenwart, P. et al. Multiple energy scales at a quantum critical point. Science 315, 969–971 (2007)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Giamarchi, T., Rüegg, C. & Tchernyshoyov, O. Bose–Einstein condensation in magnetic insulators. Nature Phys. 4, 198–204 (2008)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Feng, Y. et al. Energy dispersive X-ray diffraction of charge density waves via chemical filtering. Rev. Sci. Instrum. 76, 063913 (2005)

    ADS  Article  Google Scholar 

  29. 29

    Strempfer, J. et al. Form-factor measurements on chromium with high-energy synchrotron radiation. Eur. Phys. J. B 14, 63–72 (2000)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Rice, T. M., Barker, A. S., Halperin, B. I. & McWhan, D. B. Antiferromagnetism in chromium and its alloys. J. Appl. Phys. 40, 1337–1343 (1969)

    ADS  CAS  Article  Google Scholar 

Download references


We are grateful to J. Pluth for assistance with sample preparation, V. Prakapenka and GeoSoilEnviroCARS (Advanced Photon Source (APS), Argonne National Laboratory) for technical support and G. Aeppli for many discussions. The work at the University of Chicago was supported by the US National Science Foundation (NSF) Division of Materials Research. GeoSoilEnviroCARS is supported by the US NSF Earth Sciences and Department of Energy (DOE) Geosciences. Use of APS is supported by the US DOE Office of Basic Energy Sciences.

Author information



Corresponding author

Correspondence to T. F. Rosenbaum.

Supplementary information

Supplementary Figure

This file contains Supplementary Figure S1 with Legend. (PDF 42 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jaramillo, R., Feng, Y., Lang, J. et al. Breakdown of the Bardeen–Cooper–Schrieffer ground state at a quantum phase transition. Nature 459, 405–409 (2009).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.